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Default Matrix Creation

I am going to a party. There will be 16 guests and 4 tables with 4 chairs at
each table. There are 6 courses of food being served and after every course
served the hostess wishes to reseat people so that at the end of the 6
courses each guest sat with as many other guests as possible and minimized
sitting at the same table with any particular guest. Anyone have an idea how
to create code to do this?
 
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